This invention relates to an accelerometer, in which the elastic restraint of the reference mass is decreased or eliminated by means of oscillation, to improve the ability to accurately measure position with the accelerometer.
A rigid body has six degrees of freedom: three are translational and three are rotational. In a practical accelerometer, mainly for purposes of ruggedness, it is desirable to rigidly constrain five of the six degrees of freedom and allow the reference mass only one degree of freedom. An unrestrained single degree of freedom reference mass could in principle directly sense displacements of the accelerometer housing with respect to the reference mass along a single axis. However, in all but the most benign applications the single degree of freedom is partially constrained by an elastic restraint combined with viscous damping. In the case of an elastically restrained degree of freedom, a bias in the read-out that senses the reference mass displacement with respect to the accelerometer housing contributes the principal error mechanism. This read-out bias causes instrument errors that are proportional to acceleration, resulting in displacement errors that grow quadratically with time. In the case of viscous damping, the errors due to a random bias in the read-out are proportional to velocity, and thus the displacement error grows linearly with time.
Dynamic tuning of accelerometers by means of a spinning, elastic, universal joint has been a part of the prior art for many years. This invention is applicable to instruments with non-spinning reference masses. A typical, prior art, single degree of freedom accelerometer with an elastically restrained, pendulous, reference mass consists of a reference mass, M, suspended on elastic pivot flexures, which hold the reference mass suspended inside a housing. An acceleration of the housing in the sensing direction causes the housing to move relative to the reference mass. This exerts a torque on the pendulous reference mass through the elastic flexure pivots and also through any viscous medium in the gaps between the stationary and moving members, causing the flexure pivots to bend. The resulting motion of the reference mass with respect to the housing is detected by suitable displacement sensors, and a force is applied to re-center the reference mass.
A problem addressed by this invention is that in the prior art soft flexures are needed to increase the sensitivity of the accelerometer, while stiff flexures are required to provide ruggedness and to constrain the unused five degrees of freedom. These conflicting requirements cannot both be satisfied, and this is a perennial limitation of flexure suspended reference masses. Other approaches to solve this problem are typically: (1) float the pendulous mass in a neutrally buoyant viscous fluid, which is expensive; (2) decrease the reference mass, however, this reduces sensitivity and signal-to-noise ratio; (3) build stronger torquers to give wider dynamic range, which requires more power and bulkier instruments; (4) build in smaller gaps to increase the damping, which makes the instrument more rugged and improves read-out bias stability, however the long term drift is still dominated by the torque derived from the spring stiffness; and (5) improve the read-out stability and reduce error torques by improvements in technology and careful design. These approaches have been brought to their limits over the last several decades.
In accelerometer design it is known that eliminating the elastic restraint from the single degree of freedom reference mass greatly improves the ability to measure position accurately. For this reason, this invention provides a means to partially or fully cancel the elastic restraint by a method of dynamic tuning based on oscillation of the gimbal that supports the reference mass.
For some analytical background describing the dynamics of an elastically restrained, damped mass, let the single degree of freedom of a reference mass, M, be restrained with respect to a housing structure by a spring constant, K, and a damping constant, D, as depicted in FIG. 1. Assuming the mass has a single translational degree of freedom, the equation of motion is shown in equation 1, where x is the acceleration of the reference mass with respect to inertial space and xcex94x is the displacement of the reference mass from the spring null position. In a closed loop accelerometer, a force, F, is nominally derived from a control loop that drives xcex94x to zero. The measured force gives an estimate of the acceleration, shown in equation 2. However, a read-out that senses xcex94x is not perfect and xcex94x is not zero. This results in an extraneous rebalance force xcex94F=Kxcex94x, which translates into an acceleration error shown in equation 3. This is usually the dominant error in an accelerometer with an elastically restrained reference mass. It is this error that the tuning of this invention reduces or eliminates.
Furthermore, there is a low frequency resonance in this system that must be damped. Usually this system is highly damped and it is desirable to keep the time constant D/K as long as possible to damp out shock and vibration without destroying the sensitivity of the instrument. Dynamic tuning of this invention reduces or eliminates this resonance and provides an extremely long time constant.
The invention herein provides a dynamic tuning mechanism that replaces the mechanical spring constant, K, by a xe2x80x98tunedxe2x80x99 stiffness, Kxe2x88x92Ktuned, so the acceleration error is now given by equation 4, and the low frequency time constant is given by equation 5. By properly tuning the effective stiffness so that (Kxe2x88x92Ktuned) is zero, the acceleration error may be made to vanish and the time constant effectively goes to infinity, giving a velocity memory to the reference mass dynamics. These are properties that were only found in fluid filled instruments before this invention.
With a xe2x80x98tunedxe2x80x99 elastic restraint, the equation of motion at low frequencies is given by equation 6. The measured force still gives an estimate of the acceleration shown in equation 7. However, a read-out bias error, Dx, now contributes nothing to the acceleration error, but rather contributes a velocity error shown in equation 8 which in practice is much more benign than an acceleration error. In addition there are no low frequency resonances in this system, and the dynamic hang-off displacement is a measure of uncompensated velocity.
Dynamic tuning by oscillation, according to this invention, can solve all of the problems of the prior art. The reason is that the effective elastic restraint, Kxe2x88x92Ktuned, of the dynamically tuned flexures restraining the sensitive degree of freedom can be made several orders of magnitude smaller than the mechanical stiffness, K. Therefore, a tuned flexure accelerometer of this invention can have both rugged flexures and high dynamic range simultaneously. This solves the perennial accelerometer design problem.
This invention features in one embodiment a tuned flexure accelerometer, comprising: a housing; a gimbal coupled to the housing for oscillation about a gimbal oscillation axis; a reference mass coupled by one or more pivots to the gimbal to allow pivoting motion of the reference mass relative to the gimbal about a pivot axis which is transverse to the gimbal oscillation axis, the one or more pivots having an effective elastic restraint; and means for inducing on the one or more pivots an oscillating negative elastic restraint, to reduce the effective elastic restraint of the pivots.
The means for inducing may include means for oscillating the reference mass about an inducing oscillation axis which is transverse to the pivot axis. The means for oscillating the reference mass may include means for oscillating the gimbal about the gimbal oscillation axis. The means for oscillating the reference mass may further include means for varying one of the gimbal oscillation amplitude and the gimbal oscillation frequency and the gimbal oscillation inertia. The means for oscillating the reference mass preferably includes means for varying the gimbal oscillation amplitude.
The means for oscillating the gimbal about the gimbal oscillation axis preferably oscillates the gimbal to create a negative elastic restraint which substantially fully cancels the effective elastic restraint of the one or more pivots.
The reference mass may be coupled to the gimbal by a pair of flexures. The gimbal oscillation axis may be nominally orthogonal to the pivot axis. The reference mass may be carried within the gimbal. The gimbal may comprise a generally planar structure. The reference mass may comprise a generally planar structure which is nominally coplanar with the gimbal.
The reference mass may have a null position with respect to the housing, in which case the invention may further include means for sensing the pivoting motion of the reference mass from the null position. The accelerometer may further include means, responsive to the means for sensing, for driving the reference mass closer to its null position.
In another embodiment, this invention features a tuned flexure accelerometer, comprising: a housing; a gimbal coupled to the housing for oscillation about a gimbal oscillation axis; a reference mass coupled by one or more pivots to the gimbal to allow pivoting motion of the reference mass relative to the gimbal about a pivot axis which is nominally orthogonal to the gimbal oscillation axis, the one or more pivots having an effective elastic restraint; and means for oscillating the gimbal about the gimbal oscillation axis to thereby induce on the one or more pivots an oscillating negative elastic restraint, to reduce the effective elastic restraint of the pivots.